All the important parameters of a truncated icosahedron

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All the important parameters of a truncated icosahedron (Goldberg polyhedron, G(1,1)) such as normal distances & solid angles of the faces, inner radius, outer radius, mean radius, surface area & volume have been calculated by using HCR's formula for regular polyhedrons (all five platonic solids)

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HCR’s Formula for Regular n-Polyhedrons Analysis of Truncated Icosahedron: Let there be any truncated icosahedron having 12 congruent regular pentagonal 20 congruent regular hexagonal faces each of edge length a then all the important parameters of the given truncated icosahedron are calculated as tabulated below Congruent polygonal faces No. of faces Normal distance of each face from the centre of the given truncated icosahedron Solid angle subtended by each face at the centre of the given truncated icosahedron in Ste-radian sr Regular pentagon 12 √ √ Regular hexagon 20 √ √ √ Inner inscribed radius √ √ Outer circumscribed radius √ √ Mean radius √ Surface area √ Volume √ Estimated illustrated by Mr Harish Chandra Rajpoot B Tech Mechanical Engineering M.M.M. University of Technology Gorakhpur-273010 UP India Dec 2014

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